Vine-Copula GARCH Model with Dynamic Conditional Dependence

Abstract

Constructing multivariate conditional distributions for non-Gaussian return series has been a major research agenda recently. Copula GARCH models combine the use of GARCH models and a copula function to allow flexibility on the choice of marginal distributions and dependence structures. However, it is non-trivial to define multivariate copula densities that allow dynamic dependent structures in returns. The vine-copula method has been gaining attention recently in that a multidimensional density can be decomposed into a product of conditional bivariate copulas and marginal densities. The dependence structure is interpreted individually in each copula pair. Yet, most studies have only focused on time varying correlation. In this paper, we propose a vine-copula GARCH model with dynamic conditional dependence. We develop a generic approach to specifying dynamic conditional dependence using any dependence measures. The characterization also induces multivariate conditional dependence dynamically through vine decomposition. The main idea is to incorporate dynamic conditional dependence, such as Kendall's tau and rank correlation, not to mention linear correlation, in each bivariate copula pair. The estimation is conducted through a sequential approach. Simulation experiments are performed and five Hong Kong blue chip stock data from January 2004 to December 2011 are studied. Using t and two Archimedean copulas, it is revealed that Kendall's tau and linear correlation of the stock returns vary over time, which indicates the presence of time varying properties in dependence.